From the point of view of old clients, segwit adds one coinbase output that contains the root hash of the Merkle tree that commits to the witness transaction ids. It uses 47 extra bytes per block, so technically, yes, it "wastes precious blockchain space". The blockchain on-disk can be pruned though (implemented as an experimental feature in Bitcoin Core 0.11, and with nearly full functionality in 0.12), so calling it "permanently" is not very accurate.

If you're talking about storage space used by segwit-compatible full nodes, well, obviously it will use more space, because it increases block capacity - that capacity has to go somewhere. However:

• The extra space used by witnesses is more prunable than normal block space, as it's not needed by non-validating clients.
• Has less effect on bandwidth, as light clients don't need the witness data.
• Has no effect on the UTXO set, so does not contribute to database growth and/or churn.
• Enables script versions, which will make the introduction of Schnorr signatures much easier later on, which are more space efficient than what we have now (even for simple single-key outputs/inputs).